Is it possible to switch objects while still remaining in edit mode?
You can use Outliner editor to press on the buttons next to the object name to enter Edit mode for those objects:



It's needed to press exactly that triangle button which shows mesh datablock inside of object datablock. If you click on the object name it will activate Object mode.  

Note that this won't allow to bypass switching interaction modes; there will be Edit mode toggle anyway visible in the actions history, it's just that there will be less clicks: